Question

Joe is riding a zip-line from the rampart of a castle 50 m from shore. The rampart is 20 m tall. How far will he travel, on the zip-line?

A) 30 m
B) 40 m
C) 50 m
D) 60 m

Answer 1

Using the Pythagorean theorem to find the length of the hypotenuse of a right triangle formed by the rampart's height and the distance to the shore, we calculate that Joe will travel approximately 54 meters on the zip-line, rounded to 60 meters as the closest given option.

Step-by-step explanation:

The question asks to determine how far Joe will travel on the zip-line from the rampart of a castle to the shore, given the height of the rampart. To find the distance Joe travels on the zip-line, we use the Pythagorean theorem, which relates the lengths of the sides of a right-angled triangle. In this scenario, the rampart's height (20 m) and the distance from the rampart to the shore (50 m) form the two sides of a right triangle, and the zip-line is the hypotenuse.

To calculate the length of the hypotenuse, we use the following equation:

Zip-line length = √(Height2 + Distance2)

Plugging in the numbers:

Zip-line length = √(20 m2 + 50 m2)

Zip-line length = √(400 m2 + 2500 m2)

Zip-line length = √(2900 m2)

Zip-line length = 53.85 m

Therefore, the closest answer from the given options is 60 m, indicating that Joe will travel approximately 54 meters on the zip-line, which we round up to the nearest available option.